Slope-base compensation including secondary output signals

ABSTRACT

A biosensor system determines analyte concentration from analytic and/or secondary output signals. The biosensor system adjusts a correlation for determining analyte concentrations from output signals with one or more index functions extracted from the output signals. The index functions determine at least one slope deviation or normalized slope deviation from one or more error parameters. The slope-adjusted correlation between analyte concentrations and output signals may be used to determine analyte concentrations having improved accuracy and/or precision from output signals including components attributable to bias.

REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.61/351,988 entitled “Slope-Based Compensation Including Secondary OutputSignals” filed Jun. 7, 2010, which is incorporated by reference in itsentirety.

BACKGROUND

Biosensor systems provide an analysis of a biological fluid, such aswhole blood, serum, plasma, urine, saliva, interstitial, orintracellular fluid. Typically, the systems include a measurement devicethat analyzes a sample contacting a test sensor. The sample usually isin liquid form and in addition to being a biological fluid, may be thederivative of a biological fluid, such as an extract, a dilution, afiltrate, or a reconstituted precipitate. The analysis performed by thebiosensor system determines the presence and/or concentration of one ormore analytes, such as alcohol, glucose, uric acid, lactate,cholesterol, bilirubin, free fatty acids, triglycerides, proteins,ketones, phenylalanine or enzymes, in the biological fluid. The analysismay be useful in the diagnosis and treatment of physiologicalabnormalities. For example, a diabetic individual may use a biosensorsystem to determine the glucose level in whole blood for adjustments todiet and/or medication.

Biosensor systems may be designed to analyze one or more analytes andmay use different volumes of biological fluids. Some systems may analyzea single drop of whole blood, such as from 0.25-15 microliters (μL) involume. Biosensor systems may be implemented using bench-top, portable,and like measurement devices. Portable measurement devices may behand-held and allow for the identification and/or quantification of oneor more analytes in a sample. Examples of portable measurement systemsinclude the Ascensia® Breeze® and Elite® meters of Bayer HealthCare inTarrytown, N.Y., while examples of bench-top measurement systems includethe Electrochemical Workstation available from CH Instruments in Austin,Tex.

In electrochemical biosensor systems, the analyte concentration isdetermined from an electrical signal generated by an oxidation/reductionor redox reaction of the analyte or a species responsive to the analytewhen an input signal is applied to the sample. The input signal may be apotential or current and may be constant, variable, or a combinationthereof such as when an AC signal is applied with a DC signal offset.The input signal may be applied as a single pulse or in multiple pulses,sequences, or cycles. An enzyme or similar species may be added to thesample to enhance the electron transfer from a first species to a secondspecies during the redox reaction. The enzyme or similar species mayreact with a single analyte, thus providing specificity to a portion ofthe generated output signal. A mediator may be used to maintain theoxidation state of the enzyme.

Electrochemical biosensor systems usually include a measurement devicehaving electrical contacts that connect with electrical conductors inthe test sensor. The conductors may be made from conductive materials,such as solid metals, metal pastes, conductive carbon, conductive carbonpastes, conductive polymers, and the like. The electrical conductorstypically connect to working, counter, reference, and/or otherelectrodes that extend into a sample reservoir. One or more electricalconductors also may extend into the sample reservoir to providefunctionality not provided by the electrodes.

The measurement device applies an input signal through the electricalcontacts to the electrical conductors of the test sensor. The electricalconductors convey the input signal through the electrodes into thesample present in the sample reservoir. The redox reaction of theanalyte generates an electrical output signal in response to the inputsignal. The electrical output signal from the strip may be a current (asgenerated by amperometry or voltammetry), a potential (as generated bypotentiometry/galvanometry), or an accumulated charge (as generated bycoulometry). The measurement device may have the processing capabilityto measure and correlate the output signal with the presence and/orconcentration of one or more analytes in the biological fluid.

In coulometry, a potential is applied to the sample to exhaustivelyoxidize or reduce the analyte. A biosensor system using coulometry isdescribed in U.S. Pat. No. 6,120,676. In amperometry, an electricalsignal of constant potential (voltage) is applied to the electricalconductors of the test sensor while the measured output signal is acurrent. Biosensor systems using amperometry are described in U.S. Pat.Nos. 5,620,579; 5,653,863; 6,153,069; and 6,413,411. In voltammetry, avarying potential is applied to a sample of biological fluid. In gatedamperometry and gated voltammetry, pulsed inputs may be used asdescribed in WO 2007/013915 and WO 2007/040913, respectively.

In many biosensor systems, the test sensor may be adapted for useoutside, inside, or partially inside a living organism. When usedoutside a living organism, a sample of the biological fluid may beintroduced into a sample reservoir in the test sensor. The test sensormay be placed in the measurement device before, after, or during theintroduction of the sample for analysis. When inside or partially insidea living organism, the test sensor may be continually immersed in thesample or the sample may be intermittently introduced to the strip. Thetest sensor may include a reservoir that partially isolates a volume ofthe sample or be open to the sample. When open, the strip may take theform of a fiber or other structure placed in contact with the biologicalfluid. Similarly, the sample may continuously flow through the strip,such as for continuous monitoring, or be interrupted, such as forintermittent monitoring, for analysis.

Biosensor systems may provide an analytic output signal during theanalysis of the biological fluid that includes one or multiple errors.These errors may be reflected in an abnormal output signal, such as whenone or more portions or the entire output signal is non-responsive orimproperly responsive to the analyte concentration of the sample. Theseerrors may be from one or more contributors, such as the physicalcharacteristics of the sample, the environmental aspects of the sample,the operating conditions of the system, and the like. Physicalcharacteristics of the sample include hematocrit (red blood cell)concentration, interfering substances, and the like. Interferingsubstances include ascorbic acid, uric acid, acetaminophen, and thelike. Environmental aspects of the sample include temperature and thelike. Operating conditions of the system include underfill conditionswhen the sample size is not large enough, slow-filling of the sample,intermittent electrical contact between the sample and one or moreelectrodes in the sensor strip, degradation of the reagents thatinteract with the analyte, and the like. There may be other contributorsor a combination of contributors that cause errors.

The analytic output signal is used by the biosensor system to determinethe analyte concentration of the sample. In addition to analytic outputsignals, secondary output signals may be determined from the sample orotherwise and be used by the biosensor system to reduce errors in theanalysis. Such secondary output signals may be determined from theelectrodes used to determine the analyte concentration of the sample, orfrom additional electrodes. Additional electrodes may include the samereagent composition as the electrodes used to determine the analyteconcentration of the sample, a different reagent composition, or noreagent composition. Secondary output signals also may be determinedfrom thermocouples and the like. For example, a reagent composition maybe used that reacts with an interferent or an electrode lacking reagentcomposition may be used to study one or more physical characteristics ofthe sample, such as whole blood hematocrit.

The measurement performance of a biosensor system is defined in terms ofaccuracy and/or precision. Increases in accuracy and/or precisionprovide for an improvement in measurement performance, a reduction inthe bias, of the system. Accuracy may be expressed in terms of bias ofthe sensor system's analyte reading in comparison to a reference analytereading, with larger bias values representing less accuracy. Precisionmay be expressed in terms of the spread or variance of the bias amongmultiple analyte readings in relation to a mean. Bias is the differencebetween one or more values determined from the biosensor system and oneor more accepted reference values for the analyte concentration in thebiological fluid. Thus, one or more errors in the analysis results inthe bias of the determined analyte concentration of a biosensor system.

Bias may be expressed in terms of “absolute bias” or “percent bias”.Absolute bias may be expressed in the units of the measurement, such asmg/dL, while percent bias may be expressed as a percentage of theabsolute bias value over the reference value. Under the ISO standard(ISO-2003E), absolute bias is used to express error in glucoseconcentrations less than 75 mg/dL, while percent bias is used to expresserror in glucose concentrations of 75 mg/dL and higher. The term“combined bias” (expressed as bias/%-bias) represents absolute bias forglucose concentrations less than 75 mg/dL and percent bias for glucoseconcentrations of 75 mg/dL and higher. Accepted reference values foranalyte concentrations may be obtained with a reference instrument, suchas the YSI 2300 STAT PLUS™ available from YSI Inc., Yellow Springs,Ohio.

Hematocrit bias refers to the difference between the reference glucoseconcentration obtained with a reference instrument and an experimentalglucose reading obtained from a biosensor system for samples containingdiffering hematocrit levels. The difference between the reference andvalues obtained from the system results from the varying hematocritlevel between specific whole blood samples and may be generallyexpressed as a percentage by the following equation: %Hct-Bias=100%×(G_(m)−G_(ref))/G_(ref), where G_(m) and G_(ref) are thedetermined glucose and reference glucose concentration readings,respectively, for any hematocrit level. The larger the absolute value ofthe % Hct-bias, the more the hematocrit level of the sample (expressedas % Hct: the percentage of red blood cell volume/sample volume) isreducing the accuracy and/or precision of the determined glucoseconcentration.

For example, if whole blood samples containing identical glucoseconcentrations, but having hematocrit levels of 20, 40, and 60%, areanalyzed, three different glucose readings will be reported by a systembased on one set of calibration constants (slope and intercept of the40% hematocrit containing whole blood sample, for instance). Thus, eventhough the whole blood glucose concentrations are the same, the systemwill report that the 20% hematocrit whole blood sample contains moreglucose than the 40% hematocrit whole blood sample, and that the 60%hematocrit whole blood sample contains less glucose than the 40%hematocrit whole blood sample. “Hematocrit sensitivity” is an expressionof the degree to which changes in the hematocrit level of a sampleaffect the bias values for an analysis. Hematocrit sensitivity may bedefined as the numerical values of the combined biases per percenthematocrit, thus bias/%-bias per % Hct.

Many biosensor systems include one or more methods to correct errorsassociated with an analysis. The concentration values obtained from ananalysis with an error may be inaccurate. Thus, the ability to correctthese analyses may increase the accuracy and/or precision of theconcentration values obtained. An error correction system may compensatefor one or more errors, such as a sample temperature or a samplehematocrit level, which are different from a reference temperature or areference hematocrit value.

While conventional error compensation systems balance various advantagesand disadvantages, none are ideal. Conventional systems usually aredirected to detect and respond to a particular type of error, eithertemperature or hematocrit, for example. Such systems typically do nothave the ability to compensate for multiple error sources or to use bothanalytic and secondary output signals for compensation. These systemsgenerally also lack the ability to alter the compensation for the errorbased on the output signal from a specific sample. Consequently,conventional biosensor systems may provide analysis results havingdetermined analyte concentration values outside a desired measurementperformance limit.

Accordingly, there is an ongoing need for improved biosensor systems,especially those that may provide increasingly accurate and/or precisedetermination of the concentration of the analyte in the sample. Thesystems, devices, and methods of the present invention overcome at leastone of the disadvantages associated with conventional biosensor systems.

SUMMARY

The present invention provides a biosensor system that adjusts arelation for determining analyte concentrations in a biological samplefrom analytic and/or secondary output signals with one or more indexfunction responsive to one or more errors that could bias the determinedanalyte concentrations. The bias may be represented by slope deviationsand normalized slope deviations obtained from one or more errorparameters. The slope deviations may be determined with one or moreindex functions from the error parameters. The term or terms of theindex functions may include error parameters extracted from orindependent of the analytic output signals.

In a method for determining an analyte concentration in a sample, anoutput signal responsive to the concentration of the analyte in thesample is generated. At least one slope deviation from at least oneerror parameter is determined, and the analyte concentration of thesample is determined from the at least one analytic output signal and atleast one slope compensation equation. The slope compensation equationis responsive to at least one index function and includes at least onereference correlation and at least one slope deviation. The slopecompensation equation may be used to determine the analyte concentrationof the sample by correcting an analyte concentration determined withoutthe slope compensation equation with the slope compensation equation.The analyte concentration of the sample may be determined by adjusting acorrelation relating the analytic output signal to the analyteconcentration in the biological sample with the slope compensationequation. The analyte concentration of the sample may be determined byadjusting the at least one analytic output signal with the slopecompensation equation. The at least one slope deviation may bedetermined from a predictor function f(predictor). The f(predictor)includes an index function and relates at least one error parameter tothe slope deviation value. The reaction may be an electrochemical redoxreaction.

A biosensor system for determining an analyte concentration in a sampleincludes a measurement device and a test sensor. The measurement devicehas a processor connected to a sensor interface and to a storage medium.The test sensor has a sample interface adjacent to a reservoir formed bythe sensor. The processor determines an output signal value responsiveto the concentration of the analyte in the sample from the sensorinterface. The processor determines at least one slope deviation valuefrom an error parameter and compensates the output signal value with theat least one slope deviation value and at least one referencecorrelation present in the storage medium.

A biosensor system adjusts a correlation between analyte concentrationsand output signals with at least one slope deviation value in responseto error parameters. The processor determines an analyte concentrationfrom the slope-adjusted correlation in response to an output signal fromthe sample interface.

In another method for determining an analyte concentration in a sample,one or more output signals are generated from a sample. At least onecomplex index function is determined, where the complex index functionis responsive to an error parameter obtained from a secondary outputsignal. The analyte concentration in the sample is determined from theoutput signals in response to the at least one complex index function.

Other systems, methods, features, and advantages of the invention willbe, or will become, apparent to one with skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional systems, methods, features andadvantages be included within this description and be within the scopeof the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention may be better understood with reference to the followingdrawings and description. The components in the figures are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention.

FIG. 1A represents a method for determining an analyte concentration ina sample.

FIG. 2A represents a gated pulse sequence where the input signal appliedto the working and counter electrodes includes multiple pulses.

FIG. 2B represents a gated pulse sequence where the input signal appliedto the working and counter electrodes includes multiple pulses, andwhere a second input signal is applied to an additional electrode togenerate a secondary output signal.

FIG. 2C depicts secondary output signal currents measured with anadditional electrode from multiple blood samples including 0%, 20%, 45%,or 70% Hct.

FIG. 3A depicts the correlation of ΔS with an index function responsiveto the ratio index R5/4.

FIG. 3B depicts the correlation between %-bias and an index functionrelating a ratio error parameter (R5/4) to slope.

FIG. 3C depicts slope and intercept based index functions relating theerror parameter of the secondary output signal currents measured fromthe additional electrode to the %-Hct of the sample.

FIG. 4A shows the reduction in bias for multiple whole blood samplesincluding different glucose concentrations and hematocrit contents of0%, 20%, 45% and 70%-Hct.

FIG. 4B depicts the relationship between S_(cal), S_(hyp), ΔS, A_(corr),A_(cal), and ΔA.

FIG. 5A shows the relationship between ΔS/S_(cal) and the secondaryoutput signal currents (Hct) obtained from an additional electrode formultiple whole blood samples including different glucose concentrationsand hematocrit contents of 0%, 20%, 45% and 70% Hct.

FIG. 5B shows the reduction in combined bias provided by thecompensation.

FIG. 5C compares the reduction in the combined biases resulting fromslope compensation using different index functions for the same wholeblood samples.

FIG. 6A shows the relationship between ΔS/S_(cal) and in index functionincluding the secondary output signal currents obtained from anadditional electrode (Hct) and temperature as error parameters.

FIG. 6B shows the reduction in combined bias provided by thecompensation with an index function using the secondary output signalcurrents measured from the additional electrode and temperature.

FIG. 6C depicts the correlation between a complex index function andΔS/S_(cal).

FIG. 6D shows the reduction in combined bias provided by compensationwith a complex index function.

FIG. 6E depicts the correlation between a complex index function andΔS/S_(cal).

FIG. 6F shows the reduction in combined bias provided by compensationwith a complex index function.

FIG. 7A depicts a schematic representation of a biosensor system thatdetermines an analyte concentration in a sample of a biological fluid.

DETAILED DESCRIPTION

A biosensor system adjusts a correlation for determining analyteconcentrations in a biological sample from output signals with indexfunctions extracted from intermediate signals of the analytic outputsignals and/or from secondary output signals. The intermediate signalsmay be one or more portions of the analytic output signals or the like.The secondary output signals are responsive to the physical orenvironmental characteristics of the biological sample. In addition tothe compensation system providing substantial benefits when analyzingcomplex biological samples, the compensation system may be used toimprove the measurement performance of other types of analysis.

The %-bias in the correlation of analyte concentrations with outputsignals may be represented by one or more slope deviations obtained fromone or more error parameters. Error containing portions of outputsignals are reflected in the deviation between the hypothetical slope ofthe output signals and the slope of a reference correlation. Bydetermining one or more values reflecting this deviation in slope fromone or more error parameters, the measurement performance of an analysismay be increased. Predictor functions, index functions, and/or complexindex functions correspond to the %-bias in the correlation between theanalyte concentrations and the output signals due to one or more errorsin the analysis.

Predictor functions compensate the measured analyte concentration forone or more errors in the analyte concentration analysis. Such errorscan result in bias, thus reducing the accuracy and/or precision, of thedetermined analyte concentrations. One or more predictor functions maybe used. A predictor function that perfectly correlates with the totalslope deviation would provide an ultimate total error compensation ofthe analyte concentration. Such a hypothetical, perfectly correlatedpredictor function could be used to compensate for all errors in theanalysis without having to know the exact cause of the total slopedeviation, and thus the bias of the measured analyte concentration.Predictor functions include at least one index function, and one or moreof the index functions may be complex.

An index function is responsive to at least one error parameter. Anindex function may be a calculated number that correlates with an errorparameter, such as hematocrit or temperature, and represents theinfluence of this error parameter on bias. Index functions may beexperimentally determined as a regression or other equation of the plotbetween the deviation from a reference slope and the error parameter.Thus, the index function represents the influence of the error parameteron the slope deviation. Complex index functions include combinations ofterms modified by weighing coefficients. The terms included in thecomplex index function may be selected with one or more exclusion tests.

Error parameters may be any value responsive to one or more errors inthe output signal. Error parameter may be values from the analysis ofthe analyte, such as the intermediate signals from an analytic outputsignal, or from secondary output signals independent of the analyticoutput signal, such as from thermocouple currents or voltages,additional electrode currents or voltages, and the like. Thus, the errorparameters may be extracted directly or indirectly from the outputsignal of the analysis and/or obtained independently from the analyticoutput signal. Other error parameters may be determined from these orother analytic or secondary output signals. Any error parameter may beused to form the term or terms that make up the index function, such asthose described in Intl. Pub. No. WO 2009/108239, filed Dec. 6, 2008,entitled “Slope-Based Compensation,” and the like. A more detailedtreatment of error correction using index functions and slope deviationvalues also may be found in this publication.

Slope deviations may be normalized to reduce the statistical effect ofchanges in the output signals, improve the differentiation in variationsof the output signals, standardize the measurements of the outputsignals, a combination thereof, or the like. Since the slope deviationmay be normalized, an index function also may be expressed in terms ofthe relation between slope deviation and the slope of the referencecorrelation. In normalization, the slope deviation, index function, orother parameter is adjusted (multiplied, divided, or the like) by avariable to reduce the statistical effect of changes in the parameter,improve the differentiation in variations of the parameter, standardizemeasurements of the parameter, a combination thereof, or the like. Thegreater the correlation between a predictor or index function and slopedeviation, the better the function at correcting error in the analysis.

An index function is complex when the function includes a combination ofterms modified by weighing coefficients. The combination is preferably alinear combination, but other combination methods may be used thatprovide weighing coefficients for the terms. Each term may include oneor more error parameters. A more detailed treatment of using predictorand complex index functions for analyte analysis may be found in Intl.App. No. PCT/US2009/067150, filed Dec. 8, 2009, entitled “Complex IndexFunctions.”

FIG. 1A represents a method for determining an analyte concentration ina sample of a biological fluid. In 102, the biosensor system generatessecondary and/or analytic output signals in response to anoxidation/reduction (redox) reaction of an analyte in a sample of abiological fluid. In 104, the biosensor system measures the secondaryand analytic output signals. In 106, the analyte concentration isdetermined from a slope compensation equation including at least oneindex function and the output signals. The slope compensation equationmay be used with the at least one index function and the output signalsto determine analyte concentrations in the sample from the outputsignals or alternatively may be used to correct analyte concentrationsand may provide improved measurement performance in comparison toconventional biosensors. In 108, the analyte concentration may bedisplayed, stored for future reference, and/or used for additionalcalculations.

In 102 of FIG. 1A, the biosensor system generates analytic and secondaryoutput signals in response to an oxidation/reduction (redox) reaction ofan analyte in a sample of a biological fluid. The output signal may begenerated using an electrochemical or optical sensor system.

In 104 of FIG. 1A, the biosensor system measures the secondary and/oranalytic output signals. The system may measure the output signalscontinuously or intermittently. For example, the biosensor system maymeasure the analytic output signal intermittently during the pulses of agated amperometric input signal, resulting in multiple current valuesrecorded during each pulse. Secondary output signals may be measuredbefore, during, or after the analytic output signals are measured. Thesystem may show output signals on a display and/or may store one or moreoutput signal or portions of the output signals in a memory device.

FIG. 2A represents a gated pulse sequence where the input signal appliedto the working and counter electrodes includes multiple pulses. Theanalytic output signal current values resulting from the pulses aredepicted above each pulse. The intermediate signal current values aredepicted as solid circles. Each of the i values is a current value ofthe analytic output signal responsive to the input signal. The firstnumber in the subscript of the i values denotes the pulse number, whilethe second number in the subscript denotes the order of the outputsignal as the current values were measured. For example, i_(2,3) denotesthe third current value measured for the second pulse.

Index functions may include ratios extracted from the intermediateanalytic output signals as depicted in FIG. 2A. For example, theintermediate signal values may be compared within an individualpulse-signal decay cycle, to provide inter-pulse ratios such as ratiosR3=i_(3,3)/i_(3,1), R4=i_(4,3)/i_(4,1), and the like. In anotherexample, the intermediate signal values may be compared between separatepulse-signal decay cycles, such as ratios R3/2=i_(3,3)/i_(2,3),R4/3=i_(4,3)/i_(3,3), and the like.

Index functions also may include combinations of ratios extracted fromthe analytic output signal depicted in FIG. 2A. In one example, an indexfunction may include a ratio of ratios, such as Ratio3/2=R3/R2,Ratio4/3=R4/R3, and the like. In another example, an index function mayinclude a combination of indices. For example, a combination index,Index-1, may be represented as Index-1=R4/3−Ratio3/2. In anotherexample, a combination index Index-2 may be represented asIndex-2=(R4/3)^(p)−(Ratio3/2)^(q), where p and q independently arepositive numbers.

FIG. 2B represents a gated pulse sequence where the input signal appliedto the working and counter electrodes includes multiple pulses, andwhere a second input signal is applied to an additional electrode togenerate a secondary output signal. The input signal applied to theadditional electrode was applied after the completion of the analyticinput signal, but could be applied at other times. FIG. 2C depictssecondary output signal currents measured with an additional electrodefrom multiple blood samples including 0%, 20%, 45%, or 70%-Hct. In thisinstance, the correlation is expressed in the form of a second orderpolynomial, but a linear or other correlation also may be used. Forexample, the secondary output signal current measured from theadditional electrode of a test sensor including a blood sample withabout 20%-Hct content was about 2500 mV. Thus, the current values fromthe additional electrode may be used in an index function relating thecurrent values measured from the additional electrode to the %-Hct ofthe sample.

An example of a complex index function is represented as follows:ƒ(CIndex)=a ₁+(a ₂)(Hct)+(a ₃)(R4/3)+(a ₄)(R5/4)+(a ₅)(R6/5)+(a₆)(R6/4)+(a ₇)(Hct)(G _(raw))+(a ₈)(R4/3)(G _(raw))+(a ₉)(R5/3)(G_(raw))+(a ₁₀)(R6/5)(G _(raw))+(a ₁₁)(R6/4)(G _(raw))+(a₁₂)(Temp)(Hct)+(a ₁₃)(Temp)(R5/3)+(a ₁₄)(Temp)(R6/5)+(a₁₅)(Hct)(R5/4)+(a ₁₆)(Hct)(R6/5)+(a ₁₇)(Hct)(R6/4)+ . . . ,where a₁ is a constant, a₂-a₁₇ independently are weighing coefficients,G_(raw) is the determined analyte concentration of the sample withoutcompensation, Temp is temperature, and Hct is the current from anadditional electrode. Each of the weighing coefficients (a₂-a₁₇) isfollowed by its associated term.

There are at least three basic types of terms in this complex indexfunction: (1) the individual ratio indices extracted from the analyticoutput signal, such as R3/2 and R4/3, (2) the interaction terms betweenthe ratio indices extracted from the analytic output signal and thetemperature, Hct current, and/or G_(raw), such as (Temp)(R5/3) and(R4/3)(G_(raw)), and (3) temperature, Hct, or G_(raw). The terms mayinclude values other than error parameters, including G_(raw). Otherterms also may be used, including, but not limited to a combinationindex function, as previously described. The complex index function maybe solved to provide a complex index value when the terms are replacedwith the appropriate values. Statistical processing may be performed onthe multiple terms to determine one or more constants and weighingcoefficients. Statistical package software, including MINITAB (MINTAB,INC., State College, Pa.), may be used to perform the statisticalprocessing.

The terms for inclusion in the complex index function may be selectedusing one or more mathematical techniques to determine exclusion valuesfor each potential term. One or more exclusion tests are then applied tothe exclusion values to identify terms to exclude from the complex indexfunction. For example, p-values that indicate the probability ofaffecting the correlation between the complex index function and theslope deviation if the term were eliminated from the complex indexfunction may be used as exclusion values under an exclusion test toexclude terms from the complex index function. Thus, removing terms fromthe complex index function that do not affect the correlation betweenthe complex index function and the slope deviation in an undesirableway, allows the desired correlation between the complex index functionand the slope deviation. A more detailed discussion of using exclusionvalues and tests to select terms for complex index functions may befound in Intl. App. No. PCT/US2009/067150, filed Dec. 8, 2009, entitled“Complex Index Functions.”

The constant a₁ may be determined by regression or other mathematicaltechnique. While a single constant is shown in the complex indexfunction, a constant is not required; more than one may be used, and maybe equal to 0. Thus, one or more constants may or may not be included inthe complex index function. One or more constants also may be combinedwith the complex index function in forming a predictor function, such asa b₀ constant as subsequently described, for example.

While terms having weighing coefficients of one may be used, a complexindex function includes at least two terms that are modified by weighingcoefficients. Weighing coefficients are numerical values other than oneor zero. Preferably, each term including an error parameter is modifiedby a weighing coefficient. More preferably, each non-constant term ofthe complex index function is modified by a weighing coefficient.Weighing coefficients may have positive or negative values. Weighingcoefficients may be determined through the statistical processing of theexperimental data collected from a combination of multiple analyteconcentrations, different hematocrit levels, different temperatures, andthe like.

As at least two of the terms are modified by weighting coefficients,different terms that are responsive to the same error type may besynergistically combined in the complex index function. For example, ifR5/4 substantially describes the hematocrit content of the sample athigh hematocrit (about 40% to about 70%), while the current valueobtained from the additional electrode substantially describes thehematocrit content of the sample at low hematocrit (about 10% to about40%), the weighting coefficients can assign the appropriate “blend” ofthese terms to provide the desired increase in measurement performance.Additionally, the ability of any one bad term, such as an incorrectreading from the additional electrode, to adversely affect themeasurement performance of the analysis may be reduced.

In 106 of FIG. 1A, the analyte concentration of the sample may bedetermined from a slope compensation equation including at least oneindex function and the output signals. The index function may form partof a predictor function and may be complex. The index function mayrelate slope or intercept to an error parameter. Index functions, inaddition to reference correlation equations, may be pre-determined andstored in the biosensor system. Error parameter values may be determinedbefore, during, or after the analysis.

FIG. 3A depicts the correlation of ΔS with an index function responsiveto the index R5/4 error parameter. FIG. 3B depicts the correlationbetween %-bias and the index R5/4, an error parameter, where theregression equation is the index function. In FIG. 3B, the ratioparameter R5/4 represents the relationship between the analytic outputsignal currents generated by the analyte in response to the 4^(th) and5^(th) pulses of a gated amperometry pulse sequence including 7 pulses.The ratio error parameter R5/4 is an example of an error parameterdetermined from an analytic output signal.

FIG. 3C depicts slope and intercept based index functions relating theerror parameter of the secondary output signal currents measured fromthe additional electrode to the %-Hct of the sample. The currentsmeasured from the additional electrode are an example of an errorparameter determined from a secondary output signal. Thus, FIG. 2C maybe used to determine the %-Hct of a whole blood sample from thesecondary output signal currents of the additional electrode, while therelationship of FIG. 3C may be used to determine the slope and interceptat different %-Hct.

Slope compensation equations use a slope deviation with analytic outputsignals to provide a compensated analyte concentration in a sample. Theslope compensation equation may use at least one index functionrepresenting the slope deviation in combination with the analytic outputsignal values to provide a compensated analyte concentration. The slopecompensation equation also may use other functions and/or values torepresent the slope deviation. The slope compensation equationpreferably compensates for error by adjusting a reference correlationbetween output signals and known analyte concentrations to provide acompensated or corrected analyte concentration.

As previously discussed with regard to FIG. 2C, a secondary outputsignal in the form of a current from an additional electrode may beconsidered an error parameter describing the hematocrit content of awhole blood sample. The hematocrit content of the sample may beconsidered an error parameter because an error in concentration valuesmay arise from performing an analysis at a hematocrit content other thanthat at which the reference correlation was determined. The hematocritcontent of the sample may be determined from any source, such as anelectrode, calculated estimates, and the like. Thus, f(Index)_(Hct)relates hematocrit sample content to the slope deviation between thereference correlation slope determined at a reference hematocrit contentand the hypothetical slope of the line that would provide the hematocritaffected analyte concentration at the hematocrit content at which theanalysis was performed. Similarly, g(Index)_(Hct) relates hematocritsample content to the deviation in intercept between the referencecorrelation intercept determined at a reference hematocrit content andthe hypothetical intercept of the line that would provide the hematocritaffected analyte concentration at the hematocrit content at which theanalysis was performed. The slope index function for hematocritf(Index)_(Hct) and/or the intercept index function for hematocritg(Index)_(Hct) may be stored in the biosensor system with the referencecorrelation equation.

A slope compensation equation using normalization with intercepts andhematocrit based index functions may take the form:A _(corr)=(i−Int _(x %-Hct))/S _(x %-Hct)=(i−Int _(nml)*g(Index)_(Hct))(S _(nml) *f(Index)_(Hct))  (Equation A),

where Int_(x %-Hct) is intercept at x-% Hct, S_(x %-Hct) is slope at x-%Hct, Int_(nml) is the normalized intercept, g(Index)_(Hct) is theintercept based index function for %-Hct, S_(nml) is the normalizedslope, and f(Index)_(Hct) is the slope based index function for %-Hct.Thus, index functions are used to relate hematocrit to both slope andintercept. This relationship expresses the slope deviation attributableto the hematocrit effect in the form of normalized slopeS_(nml)=S/S_(ref-Hct) with the addition of normalized interceptInt_(nml)=Int/Int_(ref-Hct). The relationship also presumes %-Hct to bethe only error source and normalization is with respect to the reference%-Hct. However, more than one error source is likely to cause the slopeand intercept deviations. Therefore, the slope normalization is to thedeviated slope, whether originating from hematocrit or other errorsources, and is normalized by S_(cal), the overall reference correlationslope.

FIG. 4A shows the reduction in the combined bias for multiple wholeblood samples including different glucose concentrations and hematocritcontents of 0%, 20%, 45% and 70%-Hct. The current from the additionalelectrode was measured after about 5.7 seconds from the start of theanalysis. The analyses were performed at about 25.3±0.5° C. and the45%-Hct value was used as the center. In relation to Equation A, thefollowing relationships were used:S _(nml) =S _(x %-Hct) /S_(45%-Hct)=ƒ(Index)_(Hct)=−6E−05(Hct)²−0.0089(Hct)+1.5293,andInt _(nml) =Int _(x %-Hct) /Int _(45%-Hct)=g(Index)_(Hct)=−0.2143*(Hct)+11.528,where (Hct) represent the output signals in mV from the additionalelectrode, and S_(45%-Hct) and Int_(45%-Hct) are the calibration slopeand intercept at the selected center hematocrit of 45%-Hct. Thecompensation placed about 100% of the analyses within a ±10% combinedbias limit at the ideal condition of 25° C. A combined bias limit is aperformance limit reflecting the percentage of analyses falling within aselected boundary away from a reference value.

For a biosensor system having a linear or near-linear relationshipbetween analytic output signals and analyte concentration, system errormay be simplified by combining errors into the slope deviation from thereference correlation. FIG. 4B shows the relationship between S_(cal),S_(hyp), ΔS, A_(corr), A_(cal), and ΔA. Line A represents a referencecorrelation having a slope S_(cal) and relating an output signal in theform of current values from a biosensor system to analyte concentrationvalues obtained from a YSI or other reference instrument for thesamples. When used during the analysis of a sample by a biosensorsystem, the reference correlation of Line A may include analytic outputsignal current values having one or more errors that may provide aninaccurate and/or imprecise analyte concentration value. Line Brepresents an error-compensated correlation having a slope S_(hyp) andrelating current values obtained from the biosensor system with thesample analyte concentration values as obtained from the referenceinstrument. The error-compensated correlation has been adjusted ormodified to reduce or substantially eliminate the one or more errors. ΔSis the slope deviation between these correlation lines and may berepresented as a difference or by other mathematical operators. ΔA isthe difference between the uncompensated or uncorrected (A_(cal)) anderror compensated or corrected (A_(corr)) determined analyteconcentration values.

Thus, a slope compensation equation using ΔS may be represented asfollows:

$\begin{matrix}{{A_{corr} = \frac{{\mathbb{i}} - {Int}}{S_{cal} + {\Delta\; S}}},} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

where A_(corr) is the corrected analyte concentration, i is a value ofthe output signal from a biosensor system, Int is the intercept from areference correlation equation, S_(cal) is the slope from the referencecorrelation equation, and ΔS represents the deviation in slope betweenS_(cal) and a hypothetical slope of a line (S_(hyp)) for the analyticoutput signal value that provides an analyte concentration of the samplewithout error. The Int and S_(cal) values for the reference correlationequation may be implemented as a program number assignment (PNA) table,another look-up table, or the like in the biosensor system. The equationmay be simplified through normalization to eliminate the Int term. Otherslope compensation equations including at least one slope deviationvalue and the analytic output signal may be used. While the equationspresented throughout the application and claims may include an “=” sign,the sign is used to represent equivalence, relationship, prediction, orthe like.

Without compensation or correction, a specific analytic output signalvalue will provide a different sample analyte concentration from theS_(cal) reference correlation line than from the S_(hyp)error-compensated line. The A_(corr) value obtained from the S_(hyp)error-compensated line provides a more accurate value of the analyteconcentration in the sample. Thus, Equation 1 translates a currentvalue, S_(cal), and Int into the compensated analyte concentration valueA_(corr) using ΔS. In this way, the percent bias may be linked throughΔS into Equation 1. The percent bias values may be pulled toward thecenter of a bias distribution through the linkage of ΔS to the percentbias. As ΔS is responsive to bias, changing ΔS affects the amount ofbias remaining in the compensated analyte concentration of the sample.

If the value of ΔS is determined experimentally from samples andsubstituted into Equation 1, the bias in the determined analyteconcentrations of those samples will be fully compensated.Alternatively, if ΔS is substituted with a predictor function, then theability of the compensation equation to correct bias in the determinedanalyte concentration will depend on how well the value generated fromthe predictor function correlates with ΔS. In Equation 1, a predictorfunction, ƒ(predictor), may be substituted for ΔS. Thus, Equation 1 maybe rewritten as follows:

$\begin{matrix}{A_{corr} = {\frac{{\mathbb{i}} - {Int}}{S_{cal} + {\Delta\; S}} = {\frac{{\mathbb{i}} - {Int}}{S_{cal} + {f({predictor})}} = {\frac{{\mathbb{i}} - {Int}}{S_{cal} + {b_{1}*{f({Index})}} + b_{0}}.}}}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

While the predictor function, ƒ(predictor), may have the general form ofb₁*f(Index)+b₀, other values or indices may be used in combination withthe f(Index) to provide f(predictor). For example, the index functioncould be used with or without one or both of the b₁ and b₀ values toprovide the predictor function. For the theoretical situation where ΔSand the index function perfectly correlate, b₁ (representing slope) andb₀ (representing intercept) are one and zero, respectively. Multipleindex functions also may be combined to provide the ƒ(predictor), andthus, the corrected analyte concentration of the sample. Environmentaland/or physical characteristics of the sample may be included in thepredictor function, either as part of an index function, or otherwise.Similarly, secondary output signals may be included in the predictorfunction, either as part of an index function, or otherwise.

Slope deviation, ΔS, and/or related index functions may be normalized torepresent the %-bias in the correlation of analyte concentrations withanalytic output signals. Thus, the slope deviation, ΔS, in Equation 1may be normalized by the slope of the reference correlation equation,S_(cal), resulting in a compensation correlation between ΔS/S_(cal) andthe index function. Additionally, normalized slope deviation may beexpressed in multiple ways, such as by ΔS/S_(cal) or S/S_(cal), where“S” represents any slope that deviates from S_(cal). These expressionsare equivalent, differing by 1, thus, S/S_(cal)=1+ΔS/S_(cal). Therelationship where the normalized slope function S_(NML) is replacedwith an index function ƒ(Index) may be represented as follows:

$\begin{matrix}{A_{corr} = {\frac{{\mathbb{i}} - {Int}}{S_{cal}*\left( {1 + {\Delta\; S\text{/}S}} \right)} = {\frac{{\mathbb{i}} - {Int}}{S_{cal}*S_{NML}} = {\frac{{\mathbb{i}} - {Int}}{S_{cal}*{f({Index})}} = {\frac{{\mathbb{i}} - {Int}}{S_{cal}*\left( {{d_{1}*{Index}} + d_{0}} \right)}.}}}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

FIG. 5A shows the relationship between ΔS/S_(cal) and an index functionincluding the secondary output signal currents obtained from anadditional electrode (Hct). Multiple whole blood samples includingdifferent glucose concentrations and hematocrit contents of 0%, 20%, 45%and 70%-Hct were analyzed. The output current from the additionalelectrode was measured after about 5.7 seconds from the start of theanalysis. The analyses were performed at about 25.3±0.5° C. A linearrelationship having an R² value of about 0.91 was observed betweenΔS/S_(cal) and the index function ((Index)=0.000417(Hct)−0.801305.Larger R² values reflect the index function being better at describingΔS/S_(cal). From the correlation, a corrected glucose concentrationG_(corr) was determined using the equation as follows:G _(corr)=(i−Int)/[S _(cal)*(1+ƒ(index)_(Hct))]=(i−Int)/[S_(cal)*(1+0.000417(Hct)−0.801305)]  (Equation 4),where if Int is equal to or near 0, Int may be omitted from theequation.

FIG. 5B shows the reduction in combined bias provided by thecompensation using the secondary output signal currents measured fromthe additional electrode. The compensation placed about 95% of theanalyses within a ±10% combined bias limit.

FIG. 5C compares the reduction in the combined biases resulting fromslope compensation using different index functions for the whole bloodsamples used in FIG. 5A at 25° C. The graph shows the glucoseconcentrations determined from the uncorrected data (comp-0), the datacorrected only with the combined ratio indices having cross terms withG_(rata) (comp-R), with the secondary output currents obtained from anadditional electrode (comp-Hct), and the data corrected with a complexindex function including multiple ratio terms, additional electrodecurrents, and other error parameters (comp-Hct/R). Table 1, below,presents the percentage of the analyses falling within ±15.4, ±10.4, and±5.4 combined bias limits. Table 1 also presents the results obtainedfrom a complex index function including multiple ratio terms, butlacking error parameters from non-analytic output currents (comp-CI).

TABLE 1 Compensation Comparison - Iso-thermal condition Compensation±15.4 ±10.4 ±5.4 Comp-0 66.7 58.9 47.8 Comp-R 95.6 87.8 66.1 Comp-Hct100 95 77.2 Comp-Hct/R 100 100 97.2

Without compensation, the analysis provided about 67% of the determinedglucose concentrations within the approximately ±15% combined bias limitand about 48% of the glucose concentrations within the approximately ±5%combined bias limit. The complex index function alone and an indexfunction using the current values from the additional electrode eachincreased the determined glucose concentrations within the bias limit.However, it was slope compensation using the combination of a complexindex function including the additional electrode currents thatsignificantly improved the ability of the biosensor system to provideglucose concentrations within the approximately ±5% combined bias limit.

While the biosensor system without compensation brought less than halfof the analyses within the approximately ±5% combined bias limit, theComp-Hct/CI correction method brought approximately 97% of the analyseswithin the approximately ±5% combined bias limit− a greater than 100%(97−48/48*100) improvement in measurement performance. By reducing thenumber of readings outside of the desired bias limit, more of thereadings obtained could be used for accurate therapy by a patient whenblood glucose is being monitored, for example. Additionally, the need todiscard and repeat the analysis by the patient also may be reduced. Forexample, at a measurement performance cut-off of an approximately ±5%combined bias limit, a patient would have to discard and repeat onlyabout 3% of the analyses performed from a glucose biosensor system usingComp-Hct/CI compensation. The same glucose biosensor system lackingcompensation would require approximately 51% of the glucose analyses tobe discarded at the approximately ±5% combined bias limit, rendering theuncompensated system effectively useless for achieving a measurementperformance cut-off of an approximately ±5% combined bias limit.

FIG. 6A shows the relationship between ΔS/S_(cal) and an index functionincluding the secondary output signal currents obtained from anadditional electrode (Hct) and temperature as error parameters. Multiplewhole blood samples including different glucose concentrations andhematocrit contents of about 0%, 20%, 45% and 70%-Hct were analyzed atabout 15, 23, and 30° C. The current from the additional electrode wasmeasured after about 7 seconds from the start of the analysis. A linearrelationship having an R² value of about 0.96 was observed betweenΔS/S_(cal) and the index functionƒ(Index)_(T, Hct)=−1.27335+0.00038423(Hct)+0.0196054(Temp)+0.00000189(Temp)(Hct).From the correlation, a corrected glucose concentration G_(corr) wasdetermined using either of following equations representing two forms ofnormalized slope deviation ΔS/S_(cal) and S/S_(cal):G _(corr)=(i−Int)/S _(cal)*[1+ƒ(Index)_(T,Hct) ]=i/S_(cal)*[1+(−1.27335+0.00038423(Hct)+0.0196054(Temp)+0.00000189(Temp)(Hct)]  (Equation5),andG _(corr)=(i−Int)/[S _(cal)*ƒ(Index)_(T,Hct) ]=i/S_(cal)*[−0.27335+0.00038423(Hct)+0.0196054(T)+0.00000189(T)(Hct)]  (Equation6),where if Int is equal to or near 0, Int may be omitted from theequation. The constant terms of the two index functions differ only by“1”, and the remaining terms and their coefficients are identical.

FIG. 6B shows the reduction in combined bias provided by thecompensation with an index function using the secondary output signalcurrents measured from the additional electrode and temperature. Themethod placed about 93% of the 23° C. analyses, about 81% of the 30° C.analyses, and about 78% of the 15° C. analyses within a ±10% combinedbias limit.

Since the secondary output signal currents from the additional electrodeand the ratio indices are responsive to the hematocrit effect, addingthe ratio indices to the index function may provide improvedcompensation of the hematocrit effect. A complex index function usingtemperature (Temp), secondary output signals from an additionalelectrode (Hct), and ratio indices extracted from the analytic outputsignals as terms was determined as follows for the same blood samples:ƒ(CIndex)_(T,HCT,Rx/y)=6.0133−0.009708(Hct)+0.84614(Temp)+0.77235(R3/2)+16.313(R4/3)−19.912(R5/3)−29.872(R6/5)+25.376R6/4−0.012671(Temp)(R3/2)−1.03025(Temp)(R5/4)+0.12934(Temp)(R5/3)−0.6397(Temp)(R6/5)+0.72278(Temp)(R6/4)−6.0217e−4(Hct)(R3/2)−0.015272(Hct)(R4/3)+0.008254(Hct)(R5/4)+0.016889(Hct)(R5/3)+0.027849(Hct)(R6/5)−0.026892(Hct)(R6/4)  (Equation7).

FIG. 6C depicts the correlation between the complex index function ofEquation 7 and ΔS/S_(cal). The R² value reflecting how well the complexindex values from the function correspond to the ΔS_(cal) values was0.9858. FIG. 6D shows the reduction in combined bias provided bycompensation with the complex index function of Equation 7. The methodplaced about 100% of the 23° C. analyses, about 98% of the 30° C.analyses, and about 98% of the 15° C. analyses within a ±10% combinedbias limit.

The correlation between ΔS/S_(cal) and the index function may beimproved by adding the raw glucose term G_(rata) to the index function.A complex index function using temperature (Temp), secondary outputsignals from an additional electrode (Hct), ratio indices extracted fromthe analytic output signals, and G_(raw) as terms was determined asfollows for the same blood samples:ƒ(CIndex)_(T,HCT,Rx/y,Graw)=27.407−(0.0138549)(Hct)−(0.89007)(R4/3)−(23.859)(R5/4)+(28.142)(R6/5)+(24.517)(R6/4)+(3.7e−7)(Hct)(G_(raw))−(0.010225)(R4/3)(G _(raw))+(0.010064)(R5/3)(G_(raw))+(0.009588)(R6/5)(G _(raw))−(0.009867)(R6/4)(G_(raw))+(5.07e−6)(Temp)(Hct)+(0.037249)(Temp)(R5/3)−(0.028559)(Temp)(R6/5)+(0.0123729)(Hct)(R5/4)+(0.0146003)(Hct)(R6/5)−(0.0128883)(Hct)(R6/4)  (Equation8).

FIG. 6E depicts the correlation between the complex index function ofEquation 8 and ΔS/S_(cal). The R² value reflecting how well the complexindex values from the function correspond to the ΔS_(cal) values was0.9953. FIG. 6F shows the reduction in combined bias provided bycompensation with the complex index function of Equation 8. The methodwas able to place about 100% of the 23° C. analyses, about 100% of the30° C. analyses, and about 98% of the 15° C. analyses within a ±10%combined bias limit. Table 2, below, compares the results from slopecompensation with the index function of Equation 5 or Equation 6 andwith the complex functions of Equation 7 and Equation 8 for the sameblood samples.

TABLE 2 Compensation comparison - Temperature and Hematocrit PerformanceIndex function Index function Index function Temperature, ° C. Criterionf(T, H) f(T, H, Rx/y) f(T, H, Rx/y, G_(raw)) 23° C. Mean %-bias −0.137−1.160 −0.684 SD, %-bias 6.014 3.409 2.566 %-in ±10% 93 100 100 %-in ±5%47 84 94 30° C. Mean %-bias −0.083 −1.345 −0.525 SD, %-bias 7.488 3.6272.052 %-in ±10% 81 98 100.0 %-in ±5% 46 88 98 15° C. Mean %-bias 1.514−0.753 1.483 SD, %-bias 6.933 5.114 3.923 %-in ±10% 78 98 98 %-in ±5% 5457 86 Overall correlation 0.9575 0.9858 0.9953 with ΔS/S_(cal), R²

At the ±10% combined bias limit, an improvement in measurementperformance of about 26% (20/78*100) was observed at the lowesttemperature of 15° C. with the addition of the ratio indices to theindex function. At 23° C. and 30° C., improvements in measurementperformance of about 21% (17/81*100) and about 8% (7/93*100) wererespectively observed with the addition of the ratio indices to theindex function. Thus, an average improvement in measurement performanceof about 18% (26+21+8/3*100) was observed across the temperature range,with the greatest improvement being observed at lower temperatures.Additional improvement was observed through the inclusion of G_(raw) andits cross terms in the index function.

At the ±5% combined bias limit, the index function lacking the ratioindexes could place less than 50% (47+46+54/3) of the analyses withinthe limit. Other than at 15° C., the addition of the ratio indexesnearly doubled the number of analyses within the ±5% combined biaslimit, making this method suitable for use in a biosensor systemproviding the measurement performance of a ±5% bias limit. The additionof G_(raw) and its cross terms provided continued improvement in the 23°and 30° C. analyses and brought the low temperature 15° C. analyses upto 86% within the ±5% combined bias limit. With an average analysisinclusion of about 93% (94+98+86/3) within the ±5% combined bias limit,the method including G_(rata) and its cross terms in the index functionwould be more suitable for use in a biosensor system providing themeasurement performance of a ±5% bias limit.

FIG. 7A depicts a schematic representation of a biosensor system 700that determines an analyte concentration in a sample of a biologicalfluid. Biosensor system 700 includes a measurement device 702 and a testsensor 704, which may be implemented in any analytical instrument,including a bench-top device, a portable or hand-held device, or thelike. The measurement device 702 and the test sensor 704 may be adaptedto implement an electrochemical sensor system, an optical sensor system,a combination thereof, or the like. The biosensor system 700 adjusts acorrelation for determining analyte concentrations from analytic andsecondary output signals with at least one slope deviation value. Theslope deviation adjusted correlations may improve the measurementperformance of the biosensor system 700 in determining the analyteconcentration of the sample. The biosensor system 700 may be utilized todetermine analyte concentrations, including those of glucose, uric acid,lactate, cholesterol, bilirubin, and the like. While a particularconfiguration is shown, the biosensor system 700 may have otherconfigurations, including those with additional components.

The test sensor 704 has a base 706 that forms a reservoir 708 and achannel 710 with an opening 712. The reservoir 708 and the channel 710may be covered by a lid with a vent. The reservoir 708 defines apartially-enclosed volume. The reservoir 708 may contain a compositionthat assists in retaining a liquid sample such as water-swellablepolymers or porous polymer matrices. Reagents may be deposited in thereservoir 708 and/or the channel 710. The reagents may include one ormore enzymes, binders, mediators, and like species. The reagents mayinclude a chemical indicator for an optical system. The test sensor 704may have other configurations.

In an optical sensor system, a sample interface 714 has an opticalportal or aperture for viewing the sample. The optical portal may becovered by an essentially transparent material. The sample interface 714may have optical portals on opposite sides of the reservoir 708.

In an electrochemical system, the sample interface 714 has conductorsconnected to a working electrode 732 and a counter electrode 734 fromwhich the analytic output signal may be measured. The sample interface714 also may include conductors connected to one or more additionalelectrodes 736 from which secondary output signals may be measured. Theelectrodes may be substantially in the same plane or in more than oneplane. The electrodes may be disposed on a surface of the base 706 thatforms the reservoir 708. The electrodes may extend or project into thereservoir 708. A dielectric layer may partially cover the conductorsand/or the electrodes. The sample interface 714 may have otherelectrodes and conductors.

The measurement device 702 includes electrical circuitry 716 connectedto a sensor interface 718 and a display 720. The electrical circuitry716 includes a processor 722 connected to a signal generator 724, anoptional temperature sensor 726, and a storage medium 728.

The signal generator 724 provides an electrical input signal to thesensor interface 718 in response to the processor 722. In opticalsystems, the electrical input signal may be used to operate or controlthe detector and light source in the sensor interface 718. Inelectrochemical systems, the electrical input signal may be transmittedby the sensor interface 718 to the sample interface 714 to apply theelectrical input signal to the sample of the biological fluid. Theelectrical input signal may be a potential or current and may beconstant, variable, or a combination thereof, such as when an AC signalis applied with a DC signal offset. The electrical input signal may beapplied as a single pulse or in multiple pulses, sequences, or cycles.The signal generator 724 also may record an output signal from thesensor interface as a generator-recorder.

The optional temperature sensor 726 determines the temperature of thesample in the reservoir of the test sensor 704. The temperature of thesample may be measured, calculated from the output signal, or assumed tobe the same or similar to a measurement of the ambient temperature orthe temperature of a device implementing the biosensor system. Thetemperature may be measured using a thermister, thermometer, or othertemperature sensing device. Other techniques may be used to determinethe sample temperature.

The storage medium 728 may be a magnetic, optical, or semiconductormemory, another storage device, or the like. The storage medium 728 maybe a fixed memory device, a removable memory device, such as a memorycard, remotely accessed, or the like.

The processor 722 implements the analyte analysis and data treatmentusing computer readable software code and data stored in the storagemedium 728. The processor 722 may start the analyte analysis in responseto the presence of the test sensor 704 at the sensor interface 718, theapplication of a sample to the test sensor 704, in response to userinput, or the like.

The processor 722 directs the signal generator 724 to provide theelectrical input signal to the sensor interface 718. The processor 722receives the sample temperature from the temperature sensor 726. Theprocessor 722 receives the output signal from the sensor interface 718.The output signal is generated in response to the reaction of theanalyte in the sample. The output signal may be generated using anoptical system, an electrochemical system, or the like. The processor722 determines slope deviation compensated analyte concentrations fromoutput signals using a correlation equation as previously discussed. Theresults of the analyte analysis may be output to the display 720 and maybe stored in the storage medium 728.

The correlation equations between analyte concentrations and outputsignals may be represented graphically, mathematically, a combinationthereof, or the like. A correlation equation may include one or moreindex functions. Correlation equations may be represented by a programnumber (PNA) table, another look-up table, or the like that is stored inthe storage medium 728. Constants and weighing coefficients also may bestored in the storage medium 728. Instructions regarding implementationof the analyte analysis may be provided by the computer readablesoftware code stored in the storage medium 728. The code may be objectcode or any other code describing or controlling the functionalitydescribed herein. The data from the analyte analysis may be subjected toone or more data treatments, including the determination of decay rates,K constants, ratios, functions, and the like in the processor 722.

In electrochemical systems, the sensor interface 718 has contacts thatconnect or electrically communicate with the conductors in the sampleinterface 714 of the test sensor 704. The sensor interface 718 transmitsthe electrical input signal from the signal generator 724 through thecontacts to the connectors in the sample interface 714. The sensorinterface 718 also transmits the output signal from the sample throughthe contacts to the processor 722 and/or signal generator 724.

In light-absorption and light-generated optical systems, the sensorinterface 718 includes a detector that collects and measures light. Thedetector receives light from the liquid sensor through the opticalportal in the sample interface 714. In a light-absorption opticalsystem, the sensor interface 718 also includes a light source such as alaser, a light emitting diode, or the like. The incident beam may have awavelength selected for absorption by the reaction product. The sensorinterface 718 directs an incident beam from the light source through theoptical portal in the sample interface 714. The detector may bepositioned at an angle such as 45° to the optical portal to receive thelight reflected back from the sample. The detector may be positionedadjacent to an optical portal on the other side of the sample from thelight source to receive light transmitted through the sample. Thedetector may be positioned in another location to receive reflectedand/or transmitted light.

The display 720 may be analog or digital. The display 720 may include aLCD, a LED, an OLED, a vacuum fluorescent, or other display adapted toshow a numerical reading. Other displays may be used. The display 720electrically communicates with the processor 722. The display 720 may beseparate from the measurement device 702, such as when in wirelesscommunication with the processor 722. Alternatively, the display 720 maybe removed from the measurement device 702, such as when the measurementdevice 702 electrically communicates with a remote computing device,medication dosing pump, and the like.

In use, a liquid sample for analysis is transferred into the reservoir708 by introducing the liquid to the opening 712. The liquid sampleflows through the channel 710, filling the reservoir 708 while expellingthe previously contained air. The liquid sample chemically reacts withthe reagents deposited in the channel 710 and/or reservoir 708.

The test sensor 702 is disposed adjacent to the measurement device 702.Adjacent includes positions where the sample interface 714 is inelectrical and/or optical communication with the sensor interface 718.Electrical communication includes the transfer of input and/or outputsignals between contacts in the sensor interface 718 and conductors inthe sample interface 714. Optical communication includes the transfer oflight between an optical portal in the sample interface 714 and adetector in the sensor interface 718. Optical communication alsoincludes the transfer of light between an optical portal in the sampleinterface 714 and a light source in the sensor interface 718.

The processor 722 receives the sample temperature from the temperaturesensor 726. The processor 722 directs the signal generator 724 toprovide an input signal to the sensor interface 718. In an opticalsystem, the sensor interface 718 operates the detector and light sourcein response to the input signal. In an electrochemical system, thesensor interface 718 provides the input signal to the sample through thesample interface 714. The processor 722 receives the output signalgenerated in response to the redox reaction of the analyte in the sampleas previously discussed.

The processor 722 determines the analyte concentration of the sample.The measurement device adjusts the correlation between analyteconcentrations and output signals with at least one slope deviationvalue. The analyte concentration is determined from the slope-adjustedcorrelation and the output signal. As described previously,normalization techniques also may be used.

While various embodiments of the invention have been described, it willbe apparent to those of ordinary skill in the art that other embodimentsand implementations are possible within the scope of the invention.

What is claimed is:
 1. A method for determining an analyte concentrationin a biological sample from a test sensor including a sample interfacehaving a working electrode and a counter electrode, an additionalelectrode and a measurement device including a processor and a signalgenerator connected to the processor, the method comprising: applying amultiple pulse electrical input signal from the signal generator to thebiological sample through the working electrode and the counterelectrode of the sample interface, generating from the multiple pulseelectrical input signal at least one analytic output signal in responseto a redox reaction of an analyte from the biological sample; generatinga secondary output signal from the biological sample from the additionalelectrode, the secondary output signal in response to the hematocritcontent of the sample, the secondary output signal being generatedindependently from the redox reaction of the analyte from the biologicalsample; determining at least one index function responsive to multipleerror parameters, the index function including: a) at least one term ofan individual ratio index based on values extracted from the analyticoutput signal, b) at least one term of the interaction between at leastone of the ratio indices based on values extracted from the analyticoutput signal, the temperature, the secondary output signal ordetermined analyte concentration of the sample without compensation, andc) at least one term including the hematocrit content determined fromthe secondary output signal; and determining the analyte concentrationin the biological sample from the at least one analytic output signaland a slope compensation equation responsive to the at least one indexfunction, wherein the slope compensation equation including at least onereference correlation between analyte concentrations and output signalvalues and at least one slope deviation from the reference correlation.2. The method of claim 1, wherein the at least one index functionincludes a term determined by an intermediate signal.
 3. The method ofclaim 1, wherein a %-bias of the determined analyte concentration is±10.4%.
 4. The method of claim 1, wherein a %-bias of the determinedanalyte concentration is ±5.4%.
 5. The method of claim 1, wherein thedetermining the analyte concentration in the biological sample includesadjusting a correlation relating the analytic output signal to theanalyte concentration in the biological sample with the slopecompensation equation.
 6. The method of claim 1, wherein the determiningthe analyte concentration in the biological sample includes determiningan analyte concentration without the slope compensation, then correctingthe analyte concentration determined without the slope compensationequation with the slope compensation equation.
 7. The method of claim 1,wherein the determining the analyte concentration in the biologicalsample includes adjusting the at least one analytic output signal withthe slope compensation equation.
 8. The method of claim 1, wherein theslope compensation equation is responsive to an intercept deviation ofthe at least one error parameter.
 9. The method of claim 1, wherein theindex function is at least one of a complex index function and a part ofa predictor function, where the slope compensation equation isresponsive to the complex index function or to the predictor function.10. The method of claim 9, wherein the predictor function is responsiveto the total slope deviation.
 11. The method of claim 1, wherein theterms selected for inclusion in the index function are determined by anexclusion test from experimental data.
 12. The method of claim 1,wherein the at least one slope deviation is responsive to a %-bias ofthe analyte concentration otherwise determined from the at least oneoutput signal.
 13. The method of claim 1, wherein the temperature isdetermined via a temperature sensor on the measurement device.
 14. Ameasurement device for determining an analyte concentration in abiological sample comprising: a sensor interface coupleable to a sampleinterface of a test sensor having a reservoir for holding the biologicalsample, a counter electrode projecting into the reservoir, a workingelectrode projecting into the reservoir and an additional electrodeprojecting into the reservoir, wherein the sample interface includesconductors connected to the counter, working and additional electrodes;a signal generator coupled to the sensor interface to generate amultiple pulse electrical input signal through the sensor interface tothe counter and working electrodes, and a secondary input signal throughthe sensor interface to the additional electrode; a storage mediumstoring a slope compensation equation, a processor coupled to the sensorinterface and the storage medium, wherein the processor operates to:receive at least one analytic output signal in response to a redoxreaction of an analyte from the biological sample; receive a secondaryoutput signal from the additional electrode, the secondary output signalin response to the hematocrit content of the sample, the secondaryoutput signal being generated independently from the redox reaction ofthe analyte from the biological sample; determine at least one indexfunction responsive to multiple error parameters, the index functionincluding: a) at least one term of an individual ratio index based onvalues extracted from the analytic output signal, c) at least one termof the interaction between at least one of the ratio indices based onvalues extracted from the at least one analytic output signal, thetemperature, secondary output signal or determined analyte concentrationof the sample without compensation, and c) at least one term includingthe hematocrit content determined from the at least one secondary outputsignal; and determine the analyte concentration in the biological samplefrom the at least one output signal and the slope compensation equationresponsive to the at least one index function, the slope compensationequation including at least one reference correlation between analyteconcentrations and output signal values and at least one slope deviationfrom the reference correlation.
 15. The measurement device of claim 14,wherein a %-bias of the determined analyte concentration is ±10.4% or±5.4%.
 16. The measurement device of claim 14, wherein the indexfunction is at least one of a complex index function and a part of apredictor function, where the slope compensation equation is responsiveto the complex index function or to the predictor function.
 17. Themeasurement device of claim 14, wherein the terms selected for inclusionin the index function are determined by an exclusion test fromexperimental data.
 18. The measurement device of claim 14, furthercomprising a temperature sensor, wherein the temperature is determinedvia the temperature sensor.